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Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategiesDec 17 2014May 05 2016Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown ... More

Multipartite entanglement detection with minimal effortDec 18 2014Oct 06 2016Certifying entanglement of a multipartite state is generally considered as a demanding task. Since an $N$ qubit state is parametrized by $4^{N}-1$ real numbers, one might naively expect that the measurement effort of generic entanglement detection also ... More

Comment on "Experimental retrodiction of trajectories in double interferometer"Jul 12 2018Jul 15 2018A comment on a misleading statement contained in [Phys. Rev. A 97, 062115 (2018)]. v2: a typo corrected

The entire history of a photonJul 20 2017Using the most basic mathematical tools, I present the full analysis of the experiment decribed in [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, {\em Phys. Rev. Lett.} {\bf 111}, 240402 (2013)]. First, I confirm that the data presented therein are ... More

Theoretical Falsification of Leggett Conjecture for Two Qubits or One QuquatNov 18 2011Jan 08 2012Recently, some attention has been paid to falsifying the Leggett model, in which global probabilities characterizing a quantum state are represented by a combination of factorisable distributions. This idea was even verified in experiments, and generalized ... More

Spectra in nested Mach-Zehnder interferometer experimentsJun 20 2018By the means of the standard quantum mechanics formalism I present an explicit derivation of the structure of power spectra in Danan {\em et al.} and Zhou {\em et al.} experiments with nested dynamically changing Mach-Zehnder interferometers. The analysis ... More

Decoherence through Spin Chains: Toy ModelAug 22 2011Aug 29 2011The description of the dynamics of closed quantum systems, governed by the Schroedinger equation at first sight seems incompatible with the Lindblad equation describing open ones. By analyzing closed dynamics of a spin-1/2 chain we reconstruct exponential ... More

One-Qubit and Two-Qubit Codes in Noisy State TransferMay 04 2009Quantum state transfer is a procedure, which allows to exchange quantum information between stationary qubit systems. It is anticipated that the transfer will find applications in solid-state quantum computing. In this contribution, we discuss the effects ... More

Subadditivity of logarithm of violation of geometric Bell inequalities for quditsFeb 20 2018Geometrical Bell Inequalities (GBIs) are the strongest known Bell inequalities for collections of qubits. However, their generalizations to other systems is not yet fully understood. We formulate GBIs for an arbitrary number $N$ of observers, each of ... More

Package of facts and theorems for efficiently generating entanglement criteria for many qubitsApr 12 2012Jun 25 2012We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds ... More

Criticism of "Asking Photons Where They Have Been"Jul 07 2014Oct 06 2016I stress that [PRL 111,240402(2013)] contains no result that need to be explained by so-called Two State Vector Formalism, and closely inspected data are in disagreement with claims of Danan, Farfurnik, Bar-Ad, and Vaidman

True Multipartite Entanglement Hardy TestMar 01 2013Dec 01 2014Quantum mechanics allows systems to be entangled with each other, which results in stronger than classical correlations. Many methods of identifying entanglement have been proposed over years, most of which are based on violating some statistical inequalities. ... More

Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategiesDec 17 2014Oct 06 2016Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown ... More

Quadratic Entanglement Criteria for QutritsDec 22 2015Oct 17 2016The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in a case of qubits. The reason is that for qubits we have a convenient description of the system by the means of the well-studied correlation ... More

N-particle nonclassicality without N-particle correlationsDec 05 2011Jan 07 2013Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, ... More

Quadratic Entanglement Criteria for QutritsDec 22 2015Oct 26 2016The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in a case of qubits. The reason is that for qubits we have a convenient description of the system by the means of the well-studied correlation ... More

Quantum Byzantine Agreement via Hardy correlations and entanglement swappingAug 07 2014We present a device-independent quantum scheme for the {\em Byzantine Generals} problem. The protocol is for three parties. Party $C$ is to send two identical one bit messages to parties $A$ and $B$. The receivers $A$ and $B$ may exchange two one bit ... More

Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradictionMay 07 2012Sep 21 2012Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell's inequalities is to assume existence of joint probability distribution for measurement results for all settings ... More

Hilbert-Schmidt distance and entanglement witnessingNov 15 2018Jan 23 2019Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. In this article we apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance (HSD) between a given state and the set of separable ... More

Entanglement conditions involving intensity correlations of optical fields: the case of multi-port interferometryMar 01 2018Normalized quantum Stokes operators introduced in [Phys. Rev. A {\bf 95}, 042113 (2017)] enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers. For a given run of an experiment the ... More

Entanglement indicators for quantum optical fields: three-mode multiport beamsplitters EPR interference experimentsJan 10 2016Mar 01 2018We generalize a new approach to entanglement conditions for light of undefined photons numbers given in [Phys. Rev. A {\bf 95}, 042113 (2017)] for polarization correlations to a broader family of interferometric phenomena. Integrated optics allows one ... More

General mapping of multi-qudit entanglement conditions to non-separability indicators for quantum optical fieldsMar 08 2019We show that any multi-qudit entanglement witness leads to a non-separability indicator for quantum optical fields, which involves intensity correlation measurements and is useful for field states of undefined photon numbers. With the approach we get, ... More

Extending Bell inequalities to more partiesDec 21 2007May 06 2008We describe a method of extending Bell inequalities from $n$ to $n+1$ parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is non trivial in the sense that the inequalities produced ... More

Two Copies of the Einstein-Podolsky-Rosen State of Light Lead to Refutation of EPR IdeasJul 28 2014Feb 18 2015Bell's theorem applies to the normalizable approximations of the original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode ... More

A classical-quantum hybrid oracle architecture for Boolean oracle identification in the noisy intermediate-scale quantum eraMay 14 2019Quantum algorithms have the potential to be very powerful. However, to exploit quantum parallelism, some quantum algorithms require an embedding of large classical data into quantum states. This embedding can cost a lot of resources, for instance by implementing ... More

Clearer visibility Hong-Ou-Mandel effect with correlation function based on rates rather than intensitiesJan 28 2016Oct 06 2016We test ideas put forward e.g in arXiv:1508.02368, which suggest that using rates in quantum optics can lead to better indicators of non-classicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered ... More

Clearer visibility Hong-Ou-Mandel effect with correlation function based on rates rather than intensitiesJan 28 2016Mar 07 2017We test ideas put forward e.g in arXiv:1508.02368, which suggest that using rates in quantum optics can lead to better indicators of non-classicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered ... More

Perfect State Transfer without State Initialization and Remote CollaborationFeb 06 2009May 09 2013We present a perfect state transfer protocol via a qubit chain with the evolution governed by the $xx$ Hamiltonian. In contrast to the recent protocol announced in [Phys. Rev. Lett. {\bf 101}, 230502 (2008)], our method does not demand any remote-cooperated ... More

Finding Traps in Non-linear Spin ArraysNov 18 2009Precise knowledge of the Hamiltonian of a system is a key to many of its applications. Tasks such state transfer or quantum computation have been well studied with a linear chain, but hardly with systems, which do not possess a linear structure. While ... More

Casimir effect for tachyonic fieldsJul 04 2003Aug 29 2003In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic field, we use ... More

Algebraic approximation of analytic sets and mappingsDec 19 2007Let {X_n} be a sequence of analytic sets converging to some analytic set X in the sense of holomorphic chains. We introduce a condition which implies that every irreducible component of X is the limit of a sequence of irreducible components of the sets ... More

The relation between the quantum games, communication complexity problems and Bell inequalitiesOct 22 2007We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding element in the ... More

Casimir effect in external magnetic fieldApr 13 2005Dec 19 2005In this paper we examine the Casimir effect for charged fields in presence of external magnetic field. We consider scalar field (connected with spinless particles) and the Dirac field (connected with 1/2-spin particles). In both cases we describe quantum ... More

The Ultraviolet-Far Infrared Energy Budget of the Gravitationally Lensed Lyman Break Galaxy MS1512-cB58Feb 12 2001A 2-hour service-mode SCUBA observation of the gravitationally-lensed Lyman break galaxy MS1512-cB58 resulted in a 3 sigma upper limit of 3.9 mJy at 850um. A comparison of this upper limit with values expected from rest-UV/optical measurements of extiction ... More

Remarks on normal basesOct 13 1997We prove that any Galois extension of commutative rings with normal basis and abelian Galois group of odd order has a self dual normal basis. Also we show that if S/R is an unramified extension of number rings with Galois group of odd order and $R$ is ... More

Nontrivial realization of the space-time translations in the theory of quantum fieldsSep 15 2010In standard quantum field theory, the one-particle states are classified by unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite dimensional (non-unitary) representations of the (homogeneous) Lorentz ... More

Modified coupling procedure for the Poincaré gauge theory of gravityJun 18 2009The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier ... More

Generalized twist deformations of Poincare and Galilei Hopf algebrasDec 09 2008The three new deformed Poincare Hopf algebras are constructed with use of twist procedure. The corresponding relativistic space-times providing the sum of canonical and Lie-algebraic type of noncommutativity are proposed. Finally, the nonrelativistic ... More

The Poincaré Gauge Theory of Gravty and the Immirzi parameterOct 27 2010The minimal coupling method proved to yield definite and correct physical predictions when applied to fundamental fermions within the framework of Yang--Mills theories of Standard Model. Similarly, the possibility of formulating gravity as the Poincar\'e ... More

F-term uplifted racetrack inflationMay 30 2010It is shown that two classes of racetrack inflation models, saddle point and inflection point ones, can be constructed in a fully supersymmetric framework with the matter field F-term as a source of supersymmetry (SUSY) breaking and uplifting. Two models ... More

Canonical, Lie-algebraic and quadratic twist deformations of Galilei groupJul 01 2008Jan 27 2009New Galilei quantum groups dual to the Hopf algebras proposed in [1] are obtained by the nonrelativistic contraction procedures. The corresponding Lie-algebraic and quadratic quantum space-times are identified with the translation sectors of considered ... More

How not to discard half of the cases in QKDAug 07 2007Aug 24 2007All known QKD protocols require the parties to discard the results when they have chosen differen bases. In this paper we show that it is not necessary. We give examples of QKD protocols that are as safe as standard ones but do not involve the discarding ... More

Twist deformations of Newton-Hooke Hopf algebrasApr 02 2009We construct five new quantum Newton-Hooke Hopf algebras with the use of Abelian twist procedure. Further we demonstrate that the corresponding deformed space-times with quantum space and classical time are periodic or expanding in time.

Quantum Information Processing with Continuous Variables and Atomic EnsemblesFeb 09 2011This thesis presents three different results in quantum information theory. The first result addresses the theoretical foundations of quantum metrology. The Heisenberg limit considered as the ultimate limit in quantum metrology sets a lower bound on how ... More

The Kadison-Singer ProblemFeb 15 2017Feb 01 2018We give self-contained presentation of results related to the Kadison-Singer problem, which was recently solved by Marcus, Spielman, and Srivastava. This problem connects with unusually large number of areas including: operator algebras (pure states), ... More

Black-body radiation for twist-deformed space-timeDec 30 2015In this article we formally investigate the impact of twisted space-time on black-body radiation phenomena, i.e. we derive the $\theta$-deformed Planck distribution function as well as we perform its numerical integration to the $\theta$-deformed total ... More

Model of hydrogen atom for twisted acceleration-enlarged Newton-Hooke space-timesDec 09 2013We define the model of hydrogen atom for twist-deformed acceleration-enlarged Newton-Hooke space-time. Further, using time-dependent perturbation theory, we find in first step of iteration procedure the solution of corresponding Schroedinger equation ... More

Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equationSep 29 2013Apr 02 2014In this work the correspondence between the semiclassical limit of the DOZZ quantum Liouville theory on the torus and the Nekrasov-Shatashvili limit of the N=2* (Omega-deformed) U(2) super-Yang-Mills theory is used to propose new formulae for the accessory ... More

Classification of automatic software build methodsMay 21 2013The process of creating working software from source code and other components (like libraries, database files, etc.) is called "software build". Apart from linking and compiling, it can include other steps like automated testing, static code analysis, ... More

t-t'-J-U model in mean-field approximation: Coexistence of superconductivity and antiferromagnetismNov 07 2014We discuss the $t$-$J$-$U$ model in the mean-field approximation. The role of spin-exchange coupling $J$ and the second nearest hopping $t'$ are examined in the context of the coexistence of superconductivity (SC) and antiferromagnetism (AF). Stability ... More

Homomorphism reconfiguration via homotopyAug 12 2014Mar 24 2017We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring throughout. ... More

Searches for LFV and LNV Decays at LHCbJan 10 2013The paper presents the latest progress on the searches for Lepton Number Violating (LNV) B Meson decays, the Lepton Flavour Violating (LFV) decay $\Ptau^- \to \Pmu^-\Pmu^-\Pmu^+$, and the Lepton and Baryon Number Violating (LNV and BNV) decays $\Ptau^- ... More

Photoelectric effect for twist-deformed space-timeMay 18 2016In this article, we investigate the impact of twisted space-time on the photoelectric effect, i.e., we derive the $\theta$-deformed threshold frequency. In such a way we indicate that the space-time noncommutativity strongly enhances the photoelectric ... More

Twist deformation of doubly enlarged Newton-Hooke Hopf algebraApr 27 2012We provide fifteen twist-deformed doubly enlarged Newton-Hooke quantum space-times. In $\tau$ approaching infinity limit the twisted doubly enlarged Galilei spaces are obtained as well.

Twisted acceleration-enlarged Newton-Hooke space-times and breaking classical symmetry phenomenaJan 25 2012We find the subgroup of classical acceleration-enlarged Newton-Hooke Hopf algebra which acts covariantly on the twisted acceleration-enlarged Newton-Hooke space-times. The case of classical acceleration-enlarged Galilei quantum group is considered as ... More

RBO Protocol: Broadcasting Huge Databases for Tiny ReceiversAug 25 2011We propose a protocol (called RBO) for broadcasting long streams of single-packet messages over radio channel for tiny, battery powered, receivers. The messages are labeled by the keys from some linearly ordered set. The sender repeatedly broadcasts a ... More

Quantum mechanics of many particles defined on twisted N-enlarged Newton-Hooke space-timesApr 25 2013We provide the quantum mechanics of many particles moving in twisted N-enlarged Newton-Hooke space-time. In particular, we consider the example of such noncommutative system - the set of M particles moving in Coulomb field of external point-like source ... More

Saturation of uncertainty relations for twisted acceleration-enlarged Newton-Hooke space-timesSep 07 2011Using Fock representation we construct states saturating uncertainty relations for twist-deformed acceleration-enlarged Newton-Hooke space-times.

13/9-approximation for Graphic TSPAug 04 2011Oct 04 2011The Travelling Salesman Problem is one the most fundamental and most studied problems in approximation algorithms. For more than 30 years, the best algorithm known for general metrics has been Christofides's algorithm with approximation factor of 3/2, ... More

Low-dimensional quantum systemsOct 17 2018We study low-dimensional quantum systems with analytical and computational methods. Firstly, the one-dimensional extended $t$-$V$ model of fermions with interactions of a finite range is investigated. The model exhibits a phase transition between liquid ... More

Acrylic purification and coatingsSep 21 2012Radon (Rn) and its decay daughters are a well-known source of background in direct WIMP detection experiments, as either a Rn decay daughter or an alpha particle emitted from a thin inner surface layer of a detector could produce a WIMP-like signal. Different ... More

On extremal positive maps acting between type I factorsDec 12 2008Dec 20 2008The paper is devoted to the problem of classification of extremal positive maps acting between $B(K)$ and $B(H)$ where $K$ and $H$ are Hilbert spaces. It is shown that every positive map with the property that $\rank \phi(P)\leq 1$ for any one-dimensional ... More

Rank properties of exposed positive mapsMar 17 2011May 10 2012Let $\cK$ and $\cH$ be finite dimensional Hilbert spaces and let $\fP$ denote the cone of all positive linear maps acting from $\fB(\cK)$ into $\fB(\cH)$. We show that each map of the form $\phi(X)=AXA^*$ or $\phi(X)=AX^TA^*$ is an exposed point of $\fP$. ... More

Circle patterns and critical Ising modelsDec 23 2017Aug 08 2019A circle pattern is an embedding of a planar graph in which each face is inscribed in a circle. We define and prove magnetic criticality of a new family of Ising models on planar graphs whose dual is a circle pattern. Our construction includes as a special ... More

Poincaré duality for Ext-groups between strict polynomial fucnctorsNov 09 2014We study relation between left and right adjoint functors to the precomposition functor. As a cosnequence we obtain various dualities in the Ext-groups in the category of strict polynomial functors.

The build-up of mass in UV-selected sub-L* galaxies at z~2Feb 09 2011Broadband spectral energy distribution (SED) fitting is used to study a deep sample of UV-selected sub-L* galaxies at z~2. They are found to be less dusty than L* galaxies, and to contribute more mass to the cosmic mass budget at this epoch than is inferred ... More

A comment on "The Computational 2D Materials Database: high-throughput modeling and discovery of atomically thin crystals"Dec 13 2018Recently, Sten Haastrup, Mikkel Strange, Mohnish Pandey, Thorsten Deilmann, Per S Schmidt, Nicki F Hinsche, Morten N Gjerding, Daniele Torelli, Peter M Larsen, Anders C Riis-Jensen, Jakob Gath, Karsten W Jacobsen, Jens Jrgen Mortensen, Thomas Olsen and ... More

Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical systemApr 26 2019In this article we provide three new twist-deformed Newtonian Schwarzschild-(Anti-)de Sitter models. They are defined on the Lie-algebraically as well as on the canonically noncommutative space-times respectively. Particularly we find the corresponding ... More

Extreme amenability of abelian $L_0$ groupsJan 03 2012We show that for any abelian topological group $G$ and arbitrary diffused submeasure $\mu$, every continuous action of $L_0(\mu,G)$ on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and ... More

Complexity of Ramsey null setsMar 31 2010We show that the set of codes for Ramsey positive analytic sets is $\mathbf{\Sigma}^1_2$-complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the set of codes for uncountable analytic sets is $\mathbf{\Sigma}^1_1$-complete. ... More

On spectra and affine strict polynomial functorsDec 31 2015We compare derived categories of the category of strict polynomial functors over a finite field and the category of ordinary endofunctors on the category of vector spaces. We introduce two intermediate categories: the category of $\infty$--affine strict ... More

Riesz transform characterization of H^1 spaces associated with certain Laguerre expansionsFeb 17 2010Nov 26 2011For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf =-\frac{d^2}{dx^2}f-\frac{alpha}{x}\frac{d}{dx}f+x^2 f. We define an atomic Hardy space H^1_{at}(X), which is a ... More

Automatic continuity for isometry groupsDec 18 2013Jan 27 2014We present a general framework for automatic continuity results for groups of isometries of metric spaces. In particular, we prove automatic continuity property for the group of isometries of the Urysohn space and the Urysohn sphere, i.e. that any homomorphism ... More

Phase transition free regions in the Ising model via the Kac-Ward operatorJun 10 2013May 17 2015We investigate the spectral radius and operator norm of the Kac-Ward transition matrix for the Ising model on a general planar graph. We then use the obtained results to identify regions in the complex plane where the free energy density limits are analytic ... More

A note on sets avoiding rational distancesJul 18 2019In this paper we shall give a short proof of the result originally obtained by Ashutosh Kumar that for each $A\subset \mathbb{R}$ there exists $B\subset A$ full in $A$ such that no distance between two distinct points from $B$ is rational. We will construct ... More

Linear systems in P^3 with low degrees and low multiplicitiesOct 12 2008We prove that the linear system of hypersurfaces in P^3 of degree d, 14 <= d <= 40, with double, triple and quadruple points in general position are non-special. This solves the cases that have not been completed in a paper by E. Ballico and M.C. Brambilla. ... More

Regularity and non-emptyness of linear systems in $\mathbb P^n$Feb 07 2008The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general position. To ... More

Atomic decompositions for Hardy spaces related to Schrödinger operatorsSep 16 2014Let L_U = -Delta+U be a Schr\"odinger operator on R^d, where U\in L^1_{loc}(R^d) is a non-negative potential and d\geq 3. The Hardy space H^1(L_U) is defined in terms of the maximal function for the semigroup K_{t,U} = exp(-t L_U), namely H^1(L_U) = {f\in ... More

Parallel Prefix Algorithms for the Registration of Arbitrarily Long Electron Micrograph SeriesDec 07 2017Recent advances in the technology of transmission electron microscopy have allowed for a more precise visualization of materials and physical processes, such as metal oxidation. Nevertheless, the quality of information is limited by the damage caused ... More

Faster Than Light CommunicationNov 04 1999Nov 16 1999This paper has been withdrawn by the author, due a crucial error in the main idea.

Algorithm to Prove Formulas for the Expected Number of Questions in Mastermind GamesAug 11 2018We close the gap in the proof (published by Chen and Lin) of formulas for the minimum number of questions required in the expected case for Mastermind and its variant called AB game, where both games are played with two pegs and $n$ colors. For this purpose, ... More

Rediscovered theorem of LuzinJul 18 2019In 1934 N. N. Luzin proved in his short (but dense) paper \textit{Sur la decomposition des ensembles} that every set $X\subseteq \mathbb{R}$ can be decomposed into two full, with respect to Lebesgue measure or category, subsets. We will try to (at least ... More

A note on ccc forcingsSep 23 2008The aim of this short note is to communicate a simple solution to the problem posed in [1] as Question 7.2.7: is it true that for every ccc $\sigma$-ideal I any I-positive Borel set contains modulo I an I-positive closed set?

Forcing, games and families of closed setsOct 13 2009We propose a new, game-theoretic, approach to the idealized forcing, in terms of fusion games. This generalizes the classical approach to the Sacks and the Miller forcing. For definable ($\mathbf{\Pi}^1_1$ on $\mathbf{\Sigma}^1_1) $\sigma$-ideals we show ... More

A dichotomy for Borel functionsOct 08 2008The dichotomy discovered by Solecki in \cite{Sol} states that any Baire class 1 function is either $\sigma$-continuous or "includes" the Pawlikowski function $P$. The aim of this paper is to give an argument which is simpler than the original proof of ... More

Approximation of maps into spheres by piecewise-regular maps of class C^kAug 21 2018Dec 13 2018The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C^k, where k is an arbitrary integer.

Special homogeneous linear systems on Hirzebruch surfacesJul 22 2009The Segre-Gimigliano-Harbourne-Hirschowitz Conjecture can be naturally formulated for Hirzebruch surfaces F_n. We show that this Conjecture holds for imposed base points of equal multiplicity bounded by 8.

Reduction method for linear systems of plane curves with base fat pointsJun 28 2006In the paper we develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne Conjecture holds for systems with base points of equal multiplicity bounded ... More

Expected term bases for generic multivariate Hermite interpolationMar 30 2005The main goal of the paper is to find an effective estimation for the minimal number of generic points in $\mathbb K^2$ for which the basis for Hermite interpolation consists of the first $\ell$ terms (with respect to total degree ordering). As a result ... More

Affine strict polynomial functors and formalityNov 13 2014We introduce the notion of affine strict polynomial functor. We show how this concept helps to understand homological behavior of the operation of Frobenius twist in the category of strict polynomial functors over a field of positive characteristic. We ... More

Special homogeneous linear systems on Hirzebruch surfaces - algorithmic issuesNov 07 2009We present algorithms used in the computational part of the article "Special homogeneous linear systems on Hirzebruch surfaces".

The planar Ising model and total positivityJun 20 2016Dec 29 2016A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph $G$. Let $a_1,\dots,a_k,b_k,\dots,b_1$ be ... More

A model of morphogen transport IINov 28 2014Apr 07 2015A model of morphogen transport consisting of two evolutionary PDEs of reaction-diffusion type and three ODEs posed on a rectangular domain is analysed. We prove that the problem is globally well-posed and that the corresponding solutions converge, as ... More

On inverse powers of graphs and topological implications of Hedetniemi's conjectureDec 08 2017We consider a natural graph operation $\Omega_k$ that is a certain inverse (formally: the right adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the $\mathbb{Z}_2$-homotopy type) of the box complex, a basic tool in ... More

The $C^0$ estimate for the quaternionic Calabi conjectureJun 11 2019We prove the $C^0$ estimate for the quaternionic Monge-Amp\`ere equation on compact hyperK\"ahler with torsion manifolds. Our goal is to provide a simpler proof than the one presented by Alesker and Shelukhin.

Gaussian approximation of moments of sums of independent random variablesMay 17 2015May 19 2015We continue the research of Lata{\l}a on improving estimates of $p$-th moments of sums of independent random variables. We generalize some of his results in the case when $2 \leq p \leq 4$ and present a combinatorial approach for even moments.

A short proof of the Kac-Ward formulaFeb 15 2015Sep 05 2015We present a short proof of the Kac-Ward formula for the partition function of the Ising model on planar graphs.

Galois theory for H-extensionsApr 29 2013We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H if both A and H are flat Mittag--Leffler modules. We also provide new criteria for subalgebras ... More

Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10Apr 08 2008In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on $\mathbb P^2$ for $m=7$, 8, 9, 10, i.e. systems of curves of given degree passing through points in general position with multiplicities at least $m,...,m,m_0$, ... More

On inverse powers of graphs and topological implications of Hedetniemi's conjectureDec 08 2017May 13 2019We consider a natural graph operation $\Omega_k$ that is a certain inverse (formally: the right adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the $\mathbb{Z}_2$-homotopy type) of the box complex, a basic tool in ... More